Marginal values (or bid prices) are widely used in revenue management practice as an aid to guiding the setting of prices at which to sell or commit perishable resources. For instance, in the airline industry, marginal values can be used by an airline reservations system for granting or denying the sale of seats on one or more flight leg departures.
Each marginal value represents the minimum price that should be accepted by a merchant to sell or commit an additional perishable resource based on a goal of maximizing profitability in the face of possibly uncertain demand. For a combination of perishable resources, the sum of individual marginal values represents the minimum acceptable price for the perishable resource combination.
Perishable resources by definition are ones that cannot be inventoried and share three common characteristics: perishability, "fixed" capacity and segmentability. Perishability means that each resource ages or becomes unavailable, and thus has no value, after a certain date, time or similar temporal event. "Fixed" capacity implies a high cost of adding an incremental unit such that capacity is regarded as static and unchanging. Segmentability refers to the ability to segment customers based on a willingness to pay using different rates and/or different purchase restrictions, such as the date of purchase relative to the date of use. Examples of perishable resources include airline seats, hotel room nights, rental car days and similar products or services such as described in L. R. Weatherford & S. E. Bodily, A Taxonomy and Research Overview of Perishable-Asset Revenue Management: Yield Management, Overbooking, and Pricing, 40 Operations Research 5, pp. 831-44 (1992), the disclosure of which is incorporated herein by reference.
One problem faced in the determination of marginal values is processing time. In the airline industry, a single airline might fly possibly thousands of flight legs (a part of a flight consisting of a single take off and landing) each day. Each flight leg requires a marginal value which is itself dependent on the particular capacity of the airplane used and the known or expected demand for that flight leg as determined by the demand for all sequences of flight legs that carry passengers from their point of origin to their point of destination. The system described herein can calculate marginal values for one departure day for a large airline in less than 15 minutes. However, prior art systems which account for these factors are constructed to calculate marginal values for all future departure days at one time, that is, during a single processing run, and require substantially more than a day (and usually three days) of calculation time.
Another problem faced is determining whether the system has converged on a final solution. Prior art systems generally determine marginal values using an iterative process whereby candidate marginal values are refined during each successive iteration until a satisfactory set of values is obtained. One prior art approach places an arbitrary limit on the number of iterations performed. This limit is used to cut down on the processing time required and to avoid problems with the system oscillating between candidate solution sets. There is no assurance that the final "solution" has actually converged. Moreover, if the limit is set too high, the processing time required becomes unnecessarily long. Conversely, if the limit is set too low, the resulting set of marginal values might be far from those that generate the maximum net revenue of the entire network.
Yet another problem faced is how to treat dependencies between individual perishable resources. In the airline industry, a combination of flight legs (known as a flight path), such as occurs whenever a passenger books a series of connecting flight legs, creates a dependency between each individual flight leg in the flight path, yet prior art systems generally overlook the effect that the flight path as a whole has on the individual marginal values. Experience with revenue management systems that take into account the passenger's flight path indicate that there is substantial value in doing so, on the order of 1% to 2% of revenue compared with conventional leg-based systems.
One further complication that has been recognized by the airline industry, yet can be found in similar industries, is that of determining marginal values for flight leg departures in a multi-dimensional problem space. Prior art hotel industry approaches were merely concerned with a one-dimensional mapping of room nights based on each guest's length of stay. In the airline industry, though, marginal values must be determined with a two-dimensional mapping of seats based on individual flight legs being associated with one or more flight paths and individual flight paths being associated with one or more flight legs.
Therefore, there is a need for a method and system for determining optimal, system-wide net revenue maximizing marginal values for perishable resources, such as seats on flight leg departures, that does not require substantial processing time yet utilizes a convergence criteria for dynamically determining whether a substantially optimal set of marginal values has been obtained. Desirably, such a method and system must also factor in dependencies between individual perishable resources, including the mapping of the determination in a multi-dimensional problem space.